1. 7.2 Solving Systems of Equations by Substitution

2. Warm Up - Solve by Graphing
y = –2x – 1
y = x + 5
2x + y = 4
(-2,3) is the solution
(3, -2) is the solution

3. Steps for Solving by Substitution
Solving Systems of Equations by Substitution
Step 2
Step 3
Step 4
Step 5
Solve for one variable in one equation.
Step 1
Substitute the resulting expression into the other equation.
Now solve that equation to get the value of the first variable.
Substitute that value into either one of the original equations and solve for the other variable.
Write the values from steps 3 and 4 as an ordered pair, (x, y), and check.

4. Example One
y = x + 1
4x + y = 6

5. Example Two
x + 2y = –1
x – y = 5

6. Example Three
2x + y = –4
x + y = –7

7. Example Four - No Solution or Infinite Solutions
y = 3x + 2
6x - 2y = -4
2x + 2y = 8
x + y = -2

8. Example Five - Real-Life Application
The difference of two numbers is 40. Six times the smaller one minus the larger one is 5. What are the two numbers?

9. Example Six - Real-Life Application
Tickets for the school play cost $6 for adults and $2 students. If 175 tickets are sold, with cash receipts of $750, how many student tickets were sold?